Abstract

In this paper, the theoretical background and development of a differential-interference contrast (DIC) x-ray optic is presented. The single-element optic is capable of high-resolution phase contrast imaging and is compatible with compact sources. It is shown that an understanding of the coherence requirements in this type of imaging is imperative and is explained in detail. The optic is capable of a wavefront separation equal to the resolution of the optic which places only minor constraints on the object illumination.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Aoki, Y Kagoshima, and Y. Suzuki, eds., X-Ray Microscopy, (The Institute of Pure and Applied Physics, Tokyo, Japan 2006).
  2. D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation, (Cambridge University Press, Cambridge 1999).
  3. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
    [CrossRef] [PubMed]
  4. C. A. Larabell and M. A. Le Gros, "X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution," Mol. Biol. Cell 15, 957-962 (2004).
    [CrossRef]
  5. G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, "Phase contrast studies of biological specimens with the X-ray microscope at BESSY," Rev. Sci. Instrum. 66, 1282-1286 (1995).
    [CrossRef]
  6. G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, "Phase contrast X-ray microscopy studies," Optik 97, 181-182 (1994).
  7. T. Wilhein, B. Kaulich, and J. Susini, "Two zone plate interference contrast microscopy at 4 keV photon energy," Opt. Commun. 193, 19-26 (2001).
    [CrossRef]
  8. T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, "Differential interference contrast X-ray microscopy with submicron resolution," Appl. Phys. Lett. 78, 2082-2084 (2001).
    [CrossRef]
  9. B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, "Differential interference contrast X-ray microscopy with twin zone plates," J. Opt. Soc. Am. A 19, 797-806 (2002).
    [CrossRef]
  10. E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, "Diffractive optical elements for differential interference contrast x-ray microscopy," Opt. Express 11, 2278-2288 (2003).
    [CrossRef] [PubMed]
  11. U. Vogt, M. Lindblom, P. A. C. Jansson, T. T. Tuohimaa, A. Holmberg, H. M. Hertz, M. Wieland, and T. Wilhein, "Single-optical-element soft-x-ray interferometry with a laser-plasma x-ray source," Opt. Lett. 30, 2167-2169 (2005).
    [CrossRef] [PubMed]
  12. C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, "Single-element objective lens for soft x-ray differential interference contrast microscopy," Opt. Lett. 31, 1564-1566 (2006).
    [CrossRef] [PubMed]
  13. P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
    [CrossRef]
  14. P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, "High-resolution compact x-ray microscopy," J. Microsc. 226, 175-181 (2007).
    [CrossRef] [PubMed]
  15. M. Bertilson, O. von Hofsten, and U. Vogt, "Compact high-resolution differential interference contrast soft x-ray microscopy," Submitted to Appl. Phys. Lett. (2007).
  16. R. D. Allen, G. B. David, and G. Nomarski, "The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy," Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193-222 (1969).
    [PubMed]
  17. J. W. Goodman, Statistical Optics, (Wiley, New York 1985).
  18. C. Preza, D. L. Snyder, and J. Conchello, "Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy," J. Opt. Soc. Am. A 16, 2185-2199 (1999).
    [CrossRef]
  19. O. von Hofsten, P. A. C. Takman, and U. Vogt, "Simulation of partially coherent image formation in a compact soft x-ray microscope," Ultramicroscopy 107, 604-609 (2007).
    [CrossRef] [PubMed]
  20. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, (Cambridge University Press, 1999).
    [PubMed]
  21. A. G. Michette, Optical Systems for Soft X Rays, (Plenum Press, New York, 1986).
    [CrossRef]

2007

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, "High-resolution compact x-ray microscopy," J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

O. von Hofsten, P. A. C. Takman, and U. Vogt, "Simulation of partially coherent image formation in a compact soft x-ray microscope," Ultramicroscopy 107, 604-609 (2007).
[CrossRef] [PubMed]

2006

2005

2004

C. A. Larabell and M. A. Le Gros, "X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution," Mol. Biol. Cell 15, 957-962 (2004).
[CrossRef]

2003

2002

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
[CrossRef]

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, "Differential interference contrast X-ray microscopy with twin zone plates," J. Opt. Soc. Am. A 19, 797-806 (2002).
[CrossRef]

2001

T. Wilhein, B. Kaulich, and J. Susini, "Two zone plate interference contrast microscopy at 4 keV photon energy," Opt. Commun. 193, 19-26 (2001).
[CrossRef]

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, "Differential interference contrast X-ray microscopy with submicron resolution," Appl. Phys. Lett. 78, 2082-2084 (2001).
[CrossRef]

1999

1995

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, "Phase contrast studies of biological specimens with the X-ray microscope at BESSY," Rev. Sci. Instrum. 66, 1282-1286 (1995).
[CrossRef]

1994

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, "Phase contrast X-ray microscopy studies," Optik 97, 181-182 (1994).

1969

R. D. Allen, G. B. David, and G. Nomarski, "The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy," Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193-222 (1969).
[PubMed]

Allen, R. D.

R. D. Allen, G. B. David, and G. Nomarski, "The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy," Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193-222 (1969).
[PubMed]

Altissimo, M.

Anderson, E. H.

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, "Single-element objective lens for soft x-ray differential interference contrast microscopy," Opt. Lett. 31, 1564-1566 (2006).
[CrossRef] [PubMed]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Attwood, D. T.

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, "Single-element objective lens for soft x-ray differential interference contrast microscopy," Opt. Lett. 31, 1564-1566 (2006).
[CrossRef] [PubMed]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Cabrini, S.

Chang, C.

Chao, W.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Cojoc, D.

Conchello, J.

David, G. B.

R. D. Allen, G. B. David, and G. Nomarski, "The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy," Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193-222 (1969).
[PubMed]

Denbeaux, G.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
[CrossRef]

Di Fabrizio, E.

Eimuller, T.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
[CrossRef]

Facci, P.

Fayard, B.

Fischer, P.

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, "Single-element objective lens for soft x-ray differential interference contrast microscopy," Opt. Lett. 31, 1564-1566 (2006).
[CrossRef] [PubMed]

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
[CrossRef]

Goll, D.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
[CrossRef]

Guttmann, P.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, "Phase contrast studies of biological specimens with the X-ray microscope at BESSY," Rev. Sci. Instrum. 66, 1282-1286 (1995).
[CrossRef]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, "Phase contrast X-ray microscopy studies," Optik 97, 181-182 (1994).

Harteneck, B. D.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Hertz, H. M.

Holmberg, A.

Jansson, P. A. C.

Johansson, G. A.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, "High-resolution compact x-ray microscopy," J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

Kaulich, B.

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, "Diffractive optical elements for differential interference contrast x-ray microscopy," Opt. Express 11, 2278-2288 (2003).
[CrossRef] [PubMed]

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, "Differential interference contrast X-ray microscopy with twin zone plates," J. Opt. Soc. Am. A 19, 797-806 (2002).
[CrossRef]

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, "Differential interference contrast X-ray microscopy with submicron resolution," Appl. Phys. Lett. 78, 2082-2084 (2001).
[CrossRef]

T. Wilhein, B. Kaulich, and J. Susini, "Two zone plate interference contrast microscopy at 4 keV photon energy," Opt. Commun. 193, 19-26 (2001).
[CrossRef]

Larabell, C. A.

C. A. Larabell and M. A. Le Gros, "X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution," Mol. Biol. Cell 15, 957-962 (2004).
[CrossRef]

Le Gros, M. A.

C. A. Larabell and M. A. Le Gros, "X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution," Mol. Biol. Cell 15, 957-962 (2004).
[CrossRef]

Liddle, J. A.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Lindblom, M.

Niemann, B.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, "Phase contrast studies of biological specimens with the X-ray microscope at BESSY," Rev. Sci. Instrum. 66, 1282-1286 (1995).
[CrossRef]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, "Phase contrast X-ray microscopy studies," Optik 97, 181-182 (1994).

Nomarski, G.

R. D. Allen, G. B. David, and G. Nomarski, "The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy," Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193-222 (1969).
[PubMed]

Okuno, T.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
[CrossRef]

Ono, T.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
[CrossRef]

Preza, C.

Romanato, F.

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, "Differential interference contrast X-ray microscopy with twin zone plates," J. Opt. Soc. Am. A 19, 797-806 (2002).
[CrossRef]

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, "Differential interference contrast X-ray microscopy with submicron resolution," Appl. Phys. Lett. 78, 2082-2084 (2001).
[CrossRef]

Rudolph, D.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, "Phase contrast studies of biological specimens with the X-ray microscope at BESSY," Rev. Sci. Instrum. 66, 1282-1286 (1995).
[CrossRef]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, "Phase contrast X-ray microscopy studies," Optik 97, 181-182 (1994).

Sakdinawat, A.

Schmahl, G.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, "Phase contrast studies of biological specimens with the X-ray microscope at BESSY," Rev. Sci. Instrum. 66, 1282-1286 (1995).
[CrossRef]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, "Phase contrast X-ray microscopy studies," Optik 97, 181-182 (1994).

Schneider, G.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, "Phase contrast studies of biological specimens with the X-ray microscope at BESSY," Rev. Sci. Instrum. 66, 1282-1286 (1995).
[CrossRef]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, "Phase contrast X-ray microscopy studies," Optik 97, 181-182 (1994).

Schutz, G.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
[CrossRef]

Snyder, D. L.

Stollberg, H.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, "High-resolution compact x-ray microscopy," J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

Susini, J.

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, "Diffractive optical elements for differential interference contrast x-ray microscopy," Opt. Express 11, 2278-2288 (2003).
[CrossRef] [PubMed]

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, "Differential interference contrast X-ray microscopy with twin zone plates," J. Opt. Soc. Am. A 19, 797-806 (2002).
[CrossRef]

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, "Differential interference contrast X-ray microscopy with submicron resolution," Appl. Phys. Lett. 78, 2082-2084 (2001).
[CrossRef]

T. Wilhein, B. Kaulich, and J. Susini, "Two zone plate interference contrast microscopy at 4 keV photon energy," Opt. Commun. 193, 19-26 (2001).
[CrossRef]

Takman, P. A. C.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, "High-resolution compact x-ray microscopy," J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

O. von Hofsten, P. A. C. Takman, and U. Vogt, "Simulation of partially coherent image formation in a compact soft x-ray microscope," Ultramicroscopy 107, 604-609 (2007).
[CrossRef] [PubMed]

Thieme, J.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, "Phase contrast studies of biological specimens with the X-ray microscope at BESSY," Rev. Sci. Instrum. 66, 1282-1286 (1995).
[CrossRef]

Tuohimaa, T. T.

Vogt, U.

von Hofsten, O.

O. von Hofsten, P. A. C. Takman, and U. Vogt, "Simulation of partially coherent image formation in a compact soft x-ray microscope," Ultramicroscopy 107, 604-609 (2007).
[CrossRef] [PubMed]

Wieland, M.

Wilhein, T.

Appl. Phys. Lett.

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, "Differential interference contrast X-ray microscopy with submicron resolution," Appl. Phys. Lett. 78, 2082-2084 (2001).
[CrossRef]

J. Microsc.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, "High-resolution compact x-ray microscopy," J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Phys. D

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, "Study of magnetic domains by magnetic soft x-ray transmission microscopy," J. Phys. D 35, 2391-2397 (2002).
[CrossRef]

Mol. Biol. Cell

C. A. Larabell and M. A. Le Gros, "X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution," Mol. Biol. Cell 15, 957-962 (2004).
[CrossRef]

Nature

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Opt. Commun.

T. Wilhein, B. Kaulich, and J. Susini, "Two zone plate interference contrast microscopy at 4 keV photon energy," Opt. Commun. 193, 19-26 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, "Phase contrast X-ray microscopy studies," Optik 97, 181-182 (1994).

Rev. Sci. Instrum.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, "Phase contrast studies of biological specimens with the X-ray microscope at BESSY," Rev. Sci. Instrum. 66, 1282-1286 (1995).
[CrossRef]

Ultramicroscopy

O. von Hofsten, P. A. C. Takman, and U. Vogt, "Simulation of partially coherent image formation in a compact soft x-ray microscope," Ultramicroscopy 107, 604-609 (2007).
[CrossRef] [PubMed]

Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik

R. D. Allen, G. B. David, and G. Nomarski, "The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy," Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193-222 (1969).
[PubMed]

Other

J. W. Goodman, Statistical Optics, (Wiley, New York 1985).

M. Bertilson, O. von Hofsten, and U. Vogt, "Compact high-resolution differential interference contrast soft x-ray microscopy," Submitted to Appl. Phys. Lett. (2007).

S. Aoki, Y Kagoshima, and Y. Suzuki, eds., X-Ray Microscopy, (The Institute of Pure and Applied Physics, Tokyo, Japan 2006).

D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation, (Cambridge University Press, Cambridge 1999).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, (Cambridge University Press, 1999).
[PubMed]

A. G. Michette, Optical Systems for Soft X Rays, (Plenum Press, New York, 1986).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

(a). A Visible light DIC microscope. (b) An x-ray DIC microscope

Fig. 2.
Fig. 2.

(a). The degree of coherence (left axis, in black) and the contrast increase (right axis, in gray) versus the coherence factor m for two shears. The arrows point to the appropriate y-axis. (b). Edge response for m=0.5 for three different shears and without DIC. The bias retardation and the phase of the object were both set to pi and there was no absorption in the object.

Fig. 3.
Fig. 3.

Bias and shear (expressed in terms of the outermost zone width) measured in the 2D PSF as a function of the position of the phase cut. As seen, the position of the phase cut affects both the shear and the bias.

Fig. 4.
Fig. 4.

(a). The calculated one-dimensional PSF from a DOE pattern (solid) compared with the PSF from the corresponding complex aperture function (dashed). The PSF calculated from the aperture of a conventional zone plate is also shown. (b) The resulting side-cut DOE.

Fig. 5.
Fig. 5.

(a, b). Simulated images using DIC zone plates and (c). using a conventional zone plate. The lower images show the corresponding zone plates. The image simulated using a side-cut DOE, (a), exhibits the best contrast.

Fig. 6.
Fig. 6.

(a). Intensity profiles of the images shown in Fig. 5. The image taken with the side-cut DIC optic where the shear is 50 nm shows the best contrast. Also shown is the phase of the object, varying between zero and pi/3. (b) Image contrast for the same spatial frequency as in (a) but for different object phase shifts. The side-cut DOE objective yields the best contrast for objects where the phase shift is smaller than 2π/3.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

f = 4 N ( Δ r ) 2 λ
k ( u , v ) = 1 2 PSF ( u + Δ u 2 , v ) exp ( i Δ θ ) + 1 2 PSF ( u Δ u 2 , v ) exp ( i Δ θ )
μ ( x 1 , y 1 ; x 2 , y 2 ) = κ e j ψ ( λ z ) 2 I ( η , ξ ) exp [ j 2 π λ ¯ z ( ( x 2 x 1 ) η + ( y 2 y 1 ) ξ ) ] d η d ξ I ( η , ξ ) d η d ξ
I image ( u , v ) = n = 1 N k ( u , v ) t ( u , v ) e i φ ( η n , ξ n )
I image ( u , v ) = n = 1 N 1 { k ̂ ( f , g ) t ̂ ( f Δ f n , g Δ g n ) } 2
C = I max I min I max + I min
m = NA condenser NA objective
A ( f , g ) = 1 ( k ( u , v ) ) = ( 2 π ) 2 k ̂ ( f , g )
A ( f , g ) = ( 2 π ) 2 cos ( Δ θ 2 π f Δ u 2 ) P S ̂ F ( f , g )
f cut = 2 Δ θ + l π 2 π Δ u
d cut r = Δ r ( 2 Δ θ + l π ) π Δ u

Metrics